Intense research works on twin-cell box-girder bridges are limited when compared to single-cell box-girder bridges and hence, not many sources are available to study the simultaneous effect of bending and torsion in them. The estimation of ultimate load in a twin-cell box-girder bridge under different modes of failure using the two existing simplified methods—namely, the space truss analogy and collapse mechanism—demands more research attention. The primary objective of this paper is to develop simplified equations for twin-cell box-girder bridges using the principles of collapse mechanism. The second main objective is to check the suitability of using space truss analogy and collapse mechanism in different modes of failure. Experimental work for studying the effects of various structural actions due to an eccentric loading on a simply supported twin-cell concrete box-girder bridge is conducted and numerical analyses are presented to understand the effect of load positions and reinforcement ratios in the failure modes.